# Unmatched Control Barrier Functions: Certainty Equivalence Adaptive Safety

arXiv: https://arxiv.org/abs/2207.13873 · HTML: https://mlsanity.com/paper/2207.13873/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2022.

## Built on by (most cited first, 4 of 4)

- [Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10497/) (2024)
- [Data-Driven Abstractions via Binary-Tree Gaussian Processes for Formal Verification](https://mlsanity.com/paper/2407.21029/) (2024)
- [BarrierBench: Evaluating Large Language Models for Safety Verification in Dynamical Systems](https://mlsanity.com/paper/2511.09363/) (2025)
- [Kernel-Based Learning of Safety Barriers](https://mlsanity.com/paper/2601.12002/) (2026)

## Abstract (arXiv)

This work applies universal adaptive control to control barrier functions to achieve forward invariance of a safe set despite the presence of unmatched parametric uncertainties. The approach combines two ideas. The first is to construct a family of control barrier functions that ensures the system is safe for all possible models. The second is to use online parameter adaptation to methodically select a control barrier function and corresponding safety controller from the allowable set. While such a combination does not necessarily yield forward invariance without additional requirements on the barrier function, we show that such invariance can be established by simply adjusting the adaptation gain online. It is also shown that the developed method is applicable to systems with safety constraints that have a relative degree greater than one. This work thus represents the first adaptive safety approach that successfully employs the certainty equivalence principle for general state constraints without sacrificing safety guarantees.